Question

The graph shows the function g(x) for a restricted domain.

Which is the function g(x) for a restricted domain?

g(x) = ; x –4
g(x) = ; x 0
g(x) = ; x –4
g(x) = ; x 0

Answer 1

`g(x) = \sqrt[3]{x+4};\ x \ge -4`

cube root graph translted 4 right and the nrestricted to x∈[-4,inf)

Answer 2

Answer: The correct option is option 3.

Step-by-step explanation:

In a graph x-axis represents the domain and y-axis represents the range of the function.

From the given graph it is noticed that the function is defined for the value
`x\geq -4`. It means the domain of the function is
`x\geq -4`.

So, the option 2nd and 4th are incorrect.

From the figure it is noticed that the value of the function is 0 at x = -4.

The value of the first function at x = -4 is -2, therefore 1st option is incorrect.

The standard equation of the given graph is
`\sqrt[3]{x}`, since the graph is shifted 4 units left along the x-axis, therefore the equation of the given graph is
`\sqrt[3]{x+4}`

So, the correct option is option 3.